Question

A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

Options

• `(9/10)^5`

• `1/2(9/10)^4`

• `1/2(9/10)^5`

• `(9/10)^5 + 1/2(9/10)^4`

Answer 1

`(9/10)^5 + 1/2(9/10)^4`

Explanation:

Here, n = 5

p = `10/100 = 1/10` and q = `1 - 1/10 = 9/10` and r ≤ 1

We know that

P(X = r) = `""^"n""C"_"r" "p"^"r" "q"^("n" - "r")`